NCERT Solutions Class 6 Maths Chapter 10 The Other Side of Zero Exercise 10.3

Exercise 10.3 in Chapter 10, "The Other Side of Zero," typically expands beyond a basic introduction and representation of integers on a number line towards double the challenge of operations on integers - typically focused on a student's ability to consolidate the rules and properties of arithmetic operations on integer values; particularly, of addition and subtraction, intending to develop the ability to reason formally from this point on without representing the whole process on a number line. Instead, students learn rules related to the properties of operations involving both positive and negative integer values. 

Ultimately, this exercise is essential for developing fluency in operations with integers (especially if intgers are used in future studies which includes algebra). Working through these question problems improves the student's speed and accuracy while making calculations involving integers, and prepares them for more complicated word problems involving integer relationships in higher-grade classes.

1.0Download NCERT Solutions of Class 6 Maths Chapter 10 The Other Side of Zero Exercise 10.3: Free PDF

Download NCERT Solutions for Class 6 Maths Chapter 10 The Other Side of Zero Exercise 10.3 in a clear, student-friendly PDF. Learn how to add and subtract integers effectively with expert guidance trusted by Allen and teachers across India.

2.0Key Concepts of Exercise 10.3

• Adding Integers: Explain the rules for adding integers that have the same sign (adding the magnitude of the number and keeping the sign) or at least different signs (subtracting the magnitude of the two numbers with keeping the sign of the larger number).
• Subtracting Integers: Consider subtraction to be the same as adding the additive inverse (for example, a−b=a+(−b)).
• Properties-ending number properties for additionFacebook- three main properties to explore: Tipp: Commutative property: (for example a+b=b+a). Associative property (for example, (a+b)+c=a+(b+c)).
• Additive Identity (Zero): When I add zero to any integer, that integer stays the same. For example, (a+0=a).
• Problem Solving with Integers: for any word problem or a real time problem; addition or subtraction of integers can be used for solving problems.

3.0NCERT Exercise Solutions Class 6 Maths Chapter 10 The Other Side of Zero : All Exercises 

4.0NCERT Class 6 Maths Chapter 10 Exercise 10.3 : Detailed Solutions

• Suppose you start with ₹ 0 in your bank account, and then you have credits of ₹ 30 , ₹ 40 , and ₹ 50 , and debits of ₹ 40 , ₹ 50 , and ₹ 60 . What is your bank account balance now? Sol. Here, Credits = ₹ $30+₹40+₹50=₹120$ and Debits $=₹40+₹50+₹60=₹150$ $\therefore$ Balance $=$ Credits - Debits = ₹ 120 - ₹ 150 = - ₹30 Therefore, your bank account balance is - ₹ 30 .
• Suppose you start with ₹ 0 in your bank account, and then you have debits of ₹ $1,2,4,8,16$, 32,64 , and 128 , and then a single credit of $₹256$. What is your bank account balance now? Sol. Here, Debits = ₹ $1+₹2+₹4+₹8+₹16+₹32+₹64+₹128=₹255$ $\therefore$ Balance $=$ Credits - Debits = ₹ 256 - ₹ 255 = ₹ 1 Therefore, your bank account balance is ₹ 1 .
• Why is it generally better to try and maintain a positive balance in your bank account? What are circumstances under which it may be worthwhile to temporarily have a negative balance? Sol. Having a positive balance in your bank account is generally better because:

• Avoids Overdraft Fees: Many banks charge fees if your account balance goes negative.
• Provide Financial Security: A positive balance ensures you have funds available for unexpected expenses or emergencies.
• Builds Good Credit History: Maintaining a positive balance can help to improve your credit score, making it easier to get loans or credit cards in the future. There might be a few specific situations where temporarily having a negative balance could be considered:
• Overdraft Protection: Some banks offer overdraft protection which can help avoid bounced checks or declared transactions.
• Planned Large Expenses: If you know you will have a large income soon and need to make essential purchases a temporary negative balance might be acceptable.

• Looking at the geographical cross section, fill in the respective heights: A. $\square$ B. $\square$ C. $\square$ D. $\square$ E. $\square$ F. $\square$ G. $\square$
  
  Teacher's Note Ask what a geographical cross section is by showing the figure in this page. It is like imagining a vertical slice taken out at some location on the Earth. This is what would be seen from a side view. Discuss the notion of 'sea level' for measuring heights and depths in geography. Sol. You will need to estimate the height of each point A to G from the graph. Look at the vertical axis to determine the height value corresponding to each point. Heights:

• $\mathrm{A}=+1500\mathrm{m}$
• $\mathrm{B}=-500\mathrm{m}$
• $\mathrm{C}=+300\mathrm{m}$
• $\mathrm{D}=-1200\mathrm{m}$
• $\mathrm{E}=+1200\mathrm{m}$
• $F=-200\mathrm{m}$
• $\mathrm{G}=+100\mathrm{m}$

• Which is the highest point in this geographical cross section? Which is the lowest point? Sol. Identify the point on the graph that reaches the height point above sea level. Point A shows the highest point. Similarly find the point that is the lowest, considering points below sea level as well. Point D shows the lowest point.
• Can you write the points $\mathrm{A},\mathrm{B},\dots ,\mathrm{G}$ in a sequence of decreasing order of heights? Can you write the points in a sequence of increasing order of heights? Sol. Based on the heights we determined in question 1, arrange the points from highest to lowest (decreasing order) $\mathrm{A}>\mathrm{E}>\mathrm{C}>\mathrm{G}>\mathrm{F}>\mathrm{B}>\mathrm{D}$ and then from lowest to highest (increasing order) $\mathrm{D}<\mathrm{B}<\mathrm{F}<\mathrm{G}<\mathrm{C}<\mathrm{E}<\mathrm{A}$.
• What is the highest point above sea level on Earth? What is its height? Sol. The highest point on Earth is Mount Everest at a height of 8848 m above sea level.
• What is the lowest point with respect to sea level on land or on the ocean floor? What is its height? (This height should be negative). Sol. The lowest known point on the Earth is Marina Trench, in the Pacific Ocean, at a depth of 11034 m below sea level.
• Do you know that there are some places in India where temperatures can go below $0^{\circ }\mathrm{C}$ ? Find out the places in India where temperatures sometimes go below $0^{\circ }\mathrm{C}$. What is common among these places? Why does it become colder there and not in other places?
  
  Sol. Places:

• Ladakh: This region is well-known for it's extremely cold winters, with temperatures often dropping below $0^{\circ }\mathrm{C}$.
• Himachal Pradesh: Some high-altitude areas in Himachal Pradesh, especially the northern parts, can experience sub-zero temperatures.
• Jammu & Kashmir: Similar to Ladakh, parts of Jammu and Kashmir, particularly the mountainous regions, face freezing temperatures.
• Sikkim: Being a mountainous state, Sikkim also witness sub-zero temperatures in certain areas.
• Arunachal Pradesh: The higher reaches of Arunachal Pradesh can experience cold conditions with temperatures below $0^{\circ }\mathrm{C}$. Common Factor: All these places are located in the Himalayan region, which is characterized by high altitudes. Reason for Colder Temperatures:
• High Altitude: As altitude increases, the temperature decreases. This is primarily due to the thinner atmosphere at higher altitudes, which results in less heat retention.
• Distance from the Equator: These regions are farther from the equator receiving less direct sunlight, leading to colder temperatures.

• Leh in Ladakh gets very cold during the winter. The following is a table of temperature readings taken during different times of the day and night in Leh on a day in November. Match the temperature with the appropriate time of the day and night.
  
  Sol.
  

5.0Key Features and Benefits Class 6 Maths Chapter 10 The Other Side of Zero : Exercise 10.3

• Mastery of Operations on Integers: Solutions provide a drill on the rules of addition and subtraction of integers, allowing students to master the operations.
• Broadening Abstract Thinking: Students learn to progress beyond visual representations on a number line to a more abstract form of understanding arithmetic with integers.
• Speed and Accuracy with Positive and Negative Integers: Repeated practice with the Solutions ensures that integer problems will be solved quickly and accurately.
• Foundation for Mathematics: These basic concepts form a strong groundwork for undergraduate mastery of civil engineering courses in algebra and other advanced math topics.
• Problem Solving: Solutions guide students in applying operations to real-world problems.
• Exam Readiness: Solutions that are from reputable publishers like Allen, follow the CBSE curriculum and exams will ensure students are prepared.